Yes, Virginia … A Leveraged Lifecycle Can Reduce Retirement Risk

When Barry Nalebuff and I showed in our new book that, historically, leveraged lifecycle investing would have safely increased investor returns by 60 percent, some critics reasonably wondered whether this was just a product of throwing more dollars into the market.  You see, for the last century, U.S. stocks experienced such a high average return relative to government bonds that if you just allocated a high enough proportion of your portfolio to stocks you were bound to come out ahead.

This is a reasonable concern – especially since there is no guarantee that the equity premium will be as high going forward.  But here’s the historical simulation that was the real a-ha moment behind our book.

Holding savings constant for a wage earner who ends up earning $100,000 at retirement, we simulated what would happen over 96 different investor cohorts from 1871-2009.  We compared a simple investment strategy of putting 75 percent of current savings in stocks (and 25 percent in government bonds) every year of a 44-year working life to an equally aggressive leveraged lifecycle strategy.  (By coincidence, the 75 percent strategy emulates the Dilbert Diversification strategy that I wrote about in my last diversification post.)

It turns out that a leveraged lifecycle – which starts with 200 percent of current savings in stock and ramps down over an investor’s life to 50 percent in stock near retirement – provides the same total amount of market exposure and hence the same amount of equity premium.  The leveraged lifecycle starts out exposing more savings to stock, albeit a small amount of savings at the beginning of an investor’s working life.  Closer to retirement, the leveraged lifecycle is less aggressive – exposing just 50 percent to stock market risk compared to the static 75 percent strategy.

So which of these two strategies is safer?  Until we wrote this book, anyone would have told you that buying stock on margin – literally mortgaging your retirement savings when young – was less safe than mixing unleveraged stock purchases with government bonds throughout your working life.

But look what we found:


The two strategies produced the same average retirement accumulation.  That shouldn’t be a surprise as we constructed the leveraged lifecycle to do just that.  The Eureka moment came when we looked at the change in the standard deviation.  Investing retirement savings on a leveraged basis when young led to a 21 percent reduction in the standard deviation of retirement savings. Even after accounting for margin calls and the heightened possibility of large early losses, the leveraged lifecycle still produced a mean-preserving reduction in risk.

This simple table is the empirical proof for the broader theoretical result that the leveraged lifecycle reduces investment risk.

Why is it producing superior risk-management results?  It’s not because we’re throwing more money at a high equity premium.  It’s simply because we’re doing a better job diversifying exposure to stock market risk across time.

This graph shows the average dollars invested in stock (across the 96 worker lives) under the two different strategies:


The blue line shows that the traditional 75 percent stock strategy rises exponentially and thus forces investors to be disproportionately exposed to the market in the last decade of their working life.  In contrast, the red line shows that the leveraged lifecycle more evenly exposes investors to stock market risk throughout their working lives.  The more even exposure provides greater diversification across time, and that’s the secret sauce behind the reduced risk.

We aren’t stock pickers.  It’s because we don’t know when the stock market is going to have a bad year or even a bad decade that we’d like to spread our exposure more evenly across time.

This simple table provides a key piece of evidence that the leveraged lifecycle represents a new diversification tool.  Now that’s diversifying “wolf-style.”


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  1. Ang Ung says:

    Please elaborate what does “200 percent of current savings” mean? Does it involve negative gearing? Thanks.


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  2. Joey says:

    I’m confused about the 200% of current savings in stock? How do I double my current savings when starting leveraged lifecycle investing?

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  3. charles says:

    And this is entirely worthless as a prediction of future returns. You are using results spit out by an unknown generator of events and seem to be making the assumption the results are span the entire domain of the possible events. What would happen to the model if something that never happened before happened next year? Using 360 days of data the turkey was pretty sure thanksgiving was going to be just another day. As attracted as I am to the idea, I’m reminded of the errors that Taleb rails against and I think I see them here.

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  4. John Hawks says:

    Until we wrote this book, anyone would have told you that buying stock on margin – literally mortgaging your retirement savings when young – was less safe than mixing unleveraged stock purchases with government bonds throughout your working life.

    You haven’t shown here that the leveraged strategy is equally “safe”, you have only shown that it gives a comparable mean return.

    “Safety” usually refers to a low risk of loss. To assess this, the standard deviation on the average return is not very informative. We need to know the shape of the distribution. Normal or non-normal? Skewed left or right? Is the mean buoyed by a small fraction of very lucky trials, or is it also the mode?

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  5. Ken says:

    To achieve 200% of current savings, you could do many things:

    1. Try to borrow 100% of your net worth (probably not likely)
    2. Invest in derivatives such as S&P 500 futures that would replicate a 200% exposure.
    3. Invest in a leveraged Exchange Traded Fund like SSO that replicates a 200% exposure.

    I am should there are other ways I don’t know.

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  6. Chris M. says:

    A.) That’s a terrible plot. You can’t read a thing on it, and you can’t zoom in.

    B.) This doesn’t take into account variable income, does it? The problem with this strategy is that you’re running really high risk early on… which, if you don’t go bankrupt or otherwise have to sell your assets before maturity, is a good idea.

    So what happens if you add uncertainty in income?

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  7. shaman says:

    Q – How many economists does it take to change a lightbulb?

    A – None. Assume a new lightbulb.

    The point being this is a useless simulation illustrating unrealistic concepts. Perhaps you should try something a bit more anchored in the real world, like this article:

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  8. RJ says:

    That’s a huge standard deviation in both cases. This is saying that one year in twenty (5%), you wound up with $250K or $300K. I don’t know that most retirees would

    Seems to me the mean is not a useful measurement to indicate safety. Given such a large standard deviation you’d want to see percentiles, maybe 5th, 25th, median and 75th. You’d also want to know worst-year case as well.

    Finally, it’s probably more useful to, to include post-retirement performance. For instance, I’d rather know what my inflation-indexed income would be from 65 to 80 at each percentile using various stategies

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